This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120900 #3 Mar 30 2012 18:36:58
%S A120900 1,1,2,6,19,62,209,722,2539,9054,32654,118876,436171,1611067,5984943,
%T A120900 22344455,83786875,315397144,1191324649,4513742858,17149228138,
%U A120900 65318912291,249356597492,953902701488,3656057618727,14037222220896
%N A120900 G.f. satisfies: A(x) = C(x)*A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).
%C A120900 Self-convolution equals A120899, which equals column 0 of triangle A120898 (cascadence of 1+2x+x^2).
%e A120900 A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 62*x^5 + 209*x^6 + 722*x^7 +...
%e A120900 = C(x) * A(x^3*C(x)^4) where
%e A120900 C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
%e A120900 is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2.
%o A120900 (PARI) {a(n)=local(A=1+x,C=(1/x*serreverse(x/(1+2*x+x^2+x*O(x^n))))^(1/2)); for(i=0,n,A=C*subst(A,x,x^3*C^4 +x*O(x^n)));polcoeff(A,n,x)}
%Y A120900 Cf. A120898, A120899, A000108.
%K A120900 nonn
%O A120900 0,3
%A A120900 _Paul D. Hanna_, Jul 14 2006